,ʞjSSKJr SSKrSSKrSSKJr SSjrS SjrSSjr SSjr g) ) annotationsN)compute_hypervolumecURSS:XaX RS::deURSn[R"URS5nUR5n[R"U[R SS24USS9n[R "U[S9n[U5Hn [R"Xv- SS9n [R"U 5n XU X'XkR5n [R"XI- [S9n SX'X]nX}nXmn[R"U SUSU 2S45USU 2S4'[R"U SX{S2S45X{S2S4'M U$)NraxisdtypeF)shapenparangecopyrepeatnewaxiszerosintrangeprodargmaxonesboolminimum)rank_i_loss_valsrank_i_indices subset_sizereference_pointn_trialssorted_indicessorted_loss_vals rect_diagsselected_indicesicontribs max_index loss_valskeeps ڦC:\Users\johnn\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.13_qbz5n2kfra8p0\LocalCache\local-packages\Python313\site-packages\optuna/_hypervolume/hssp.py_solve_hssp_2dr* sy  ! !" % *{>T>TUV>W/WW W%%a(HYY/55a89N',,.?2::q=98!LJxx 37 ; 77:8rBIIh' ,I-FG$/446 wwx|40'-% +1$&JJy|Z  TU =V$W :I:q=!$&JJy|Z TU =V$W :q=! c [R"U5(a%[R"U[R5$[R "USS2[R 4USS5n[R"X1- SS9n[R"U5n[R"X[R"X5SS2S4- SS9- 5nSnURSS:*n [R"U*5H|n Xz(a[R=oU 'M"X U:aM,U (a&XR5US'[X#SS9n X- X 'OXj[XZU5- X '[X U5nM~ U$) aLazy update the hypervolume contributions. (1) Lazy update of the hypervolume contributions S=selected_indices - {indices[max_index]}, T=selected_indices, and S' is a subset of S. As we would like to know argmax H(T v {i}) in the next iteration, we can skip HV calculations for j if H(T v {i}) - H(T) > H(S' v {j}) - H(S') >= H(T v {j}) - H(T). We used the submodularity for the inequality above. As the upper bound of contribs[i] is H(S' v {j}) - H(S'), we start to update from i with a higher upper bound so that we can skip more HV calculations. (2) A simple cheap-to-evaluate contribution upper bound The HV difference only using the latest selected point and a candidate is a simple, yet obvious, contribution upper bound. Denote t as the latest selected index and j as an unselected index. Then, H(T v {j}) - H(T) <= H({t} v {j}) - H({t}) holds where the inequality comes from submodularity. We use the inclusion-exclusion principle to calculate the RHS. Nrr rgT) assume_pareto)mathisinfr full_likeinfmaximumrrrr argsortrrmax) r%pareto_loss_values selected_vecsr hv_selectedintersec inclusive_hvsis_contrib_inf max_contribis_hv_calc_fastr$hv_pluss r)_lazy_contribs_updater?-sR. zz+||Hbff--zz,Q ];]3B=OPHGGO@qIMXXm,Nzz"''/QUO*KRS"TTHK(..q1Q6O ZZ "  (* .K1+  ; $   2 5 : : -+1 a    ++ )  gA(>  $  ++r+cFX!R:XaU$[R"USSS9upEURnXb:aX[R"UR[S9nSXu'[R "UR5U)nSXxSX&- 'X$[ XEX#5n X$)aPSolve a hypervolume subset selection problem (HSSP) via a greedy algorithm. This method is a 1-1/e approximation algorithm to solve HSSP. For further information about algorithms to solve HSSP, please refer to the following paper: - `Greedy Hypervolume Subset Selection in Low Dimensions `__ Tr) return_indexr r N)rCruniquerrrrK) rrrrrank_i_unique_loss_valsindices_of_unique_loss_valsn_uniquechosenduplicated_indices$selected_indices_of_unique_loss_valss r) _solve_hssprUs )));=99t!<8+//H.--T:.2+YY~':':;VGD?C":K$:;<%%+Jk,(  ??r+) r np.ndarrayrrVrrrrVreturnrV) r%rVr6rVr7rVrrVr8floatrWrV) __future__rr/numpyroptuna._hypervolume.wfgrr*r?rKrUr+r)r]s" 7        F44"44 4  4  4n(, (,(,(, (,  (,V!@ !@!@!@ !@  !@r+